Edge detection is among the most fundamental vision problems for its role in perceptual grouping and its wide applications. Recent advances in representation learning have led to considerable improvements in this area. Many state of the art edge detection models are learned with fully convolutional networks (FCNs). However, FCN-based edge learning tends to be vulnerable to misaligned labels due to the delicate structure of edges. While such problem was considered in evaluation benchmarks, similar issue has not been explicitly addressed in general edge learning. In this paper, we show that label misalignment can cause considerably degraded edge learning quality, and address this issue by proposing a simultaneous edge alignment and learning framework. To this end, we formulate a probabilistic model where edge alignment is treated as latent variable optimization, and is learned end-to-end during network training. Experiments show several applications of this work, including improved edge detection with state of the art performance, and automatic refinement of noisy annotations. Code and pre-trained models are available at https://github.com/Chrisding/seal.